How to best create an animation of an opening paper fan?
Here's one to try out. The base is a Plane with one vertical cut [CTRLR] and the lower vertices merged [ALTM]. It is shaped to approximate one fold of the fan. Hooks are added to the outer vertices by selecting them in Edit mode and pressing CTRLH. Once back in Object mode the hooks can be (shift) selected and moved down on the Z-Axis or scaled towards each other to create the fold.



You can later animate the Location by pressing CTRLI. The single fold can be duplicated with an array modifier using a new empty as the centre.



The centre empty rotation can also be animated with CTRLI to match the timing of the Hook movement. Of course it is cheating and if you look too closely they might not match perfectly..